A 3d simulator for nanowire field-effect sensors and
transistors including fast varying charge
concentrations at an interface is presented. This
simulator is based on a system of partial
differential equations calculating the electrostatic
potential of the whole device and the charge
concentrations in the semiconducting
nanowire. Therefore, three domains need to be
modeled. The nanowire is described by the
drift-diffusion-Poisson system, the
Poisson-Boltzmann equation is used for the
simulation of an aqueous solution, and the Poisson
equation holds in the remaining oxide. Such devices
can be used as gas sensors, and by functionalization
of the nanowire surface, i.e., by attaching probe
molecules, they can also be used for the detection
of biomolecules in aqueous solutions. Binding of
target molecules to the surface induces a field
effect due to changes of charges in a small layer
around the surface. This effect is responsible for
the sensor response and hence is of paramount
importance. A homogenization method resulting in two
jump conditions is implemented which splits the
computation into the charge of the boundary layer
and into the remaining device. In order to take into
account the geometry of the devices, 3d simulations
are necessary and hence a parallelization technique
has been developed. To include the jump conditions
of the homogenization method, a novel finite-element
tearing and interconnecting (FETI) method has been
developed. With this simulator it is possible to
solve the three dimensional and heterogeneous system
of partial differential equations with
discontinuities in feasible time using realizable
computer power. As a result, sensitivity in terms of
geometrical and physical properties can be predicted
and sensors can be improved.

Biologically sensitive field-effect transistors (BioFETs)
are a promising technology for detecting pathogens,
antigen-antibody complexes, and tumor markers. A
BioFET is studied for a biotin-streptavidin
complex. Biotin-streptavidin is used in detection
and purification of various biomolecules. The link
between the Angstrom scale of the chemical reaction
and the micrometer scale of the field effect device
is realized by homogenized interface conditions.

We use the stochastic linearized Poisson-Boltzmann equation
to model the fluctuations in nanowire field-effect
biosensors due to changes in the orientation of the
biomolecules. Different orientations of the
biomolecules with respect to the sensor surface due
to Brownian motion have different probabilities.
The probabilities of the orientations are calculated
from their electrostatic free energy. The structure
considered here is a cross section through a
rectangular silicon nanowire lying on a an oxide
surface with a back-gate contact. The oxide surface
of the nanowire is functionalized by biomolecules in
an electrolyte with an electrode. Various
combinations of PNA (peptide nucleic acid),
single-stranded DNA, and double-stranded DNA are
simulated to discuss the various states of a DNA
sensor. A charge-transport models yields the
current through the transducer that compares well
with measurements.

In this work the properties of a biotin-streptavidin BioFET
have been studied numerically with homogenized
boundary interface conditions as the link between
the oxide of the FET and the analyte which contains
the bio-sample. The biotin-streptavidin reaction
pair is used in purification and detection of
various biomolecules; the strong streptavidin-biotin
bond can also be used to attach biomolecules to one
another or onto a solid support. Thus this reaction
pair in combination with a FET as the transducer is
a powerful setup enabling the detection of a wide
variety of molecules with many advantages that stem
from the FET, like no labeling, no need of expensive
read-out devices, the possibility to put the signal
amplification and analysis on the same chip, and
outdoor usage without the necessity of a lab.

Device-level simulation capabilities have been developed to
self-consistently model the Si-nanowire (NW)
biosensor systems. Our numerical study demonstrates
that by introducing electro-diffusion current flow
in the electrolyte solutions, the electrostatic
screening of the biological charge can be
significantly suppressed; an improvement of the
sensed signal strength by more than approximately 10
times is indicated. Based on such an operation
principle, the screening-induced performance limits
on Si-NW biosensors can be overcome.

In this paper a bottom-up approach for modeling field-effect
Biosensors (BioFETs) is developed. Starting from the
given positions of charged atoms, of a given
molecule, the charge and the dipole moment of a
single molecule are calculated. This charge and
dipole moment are used to calculate the mean surface
density and mean dipole moment at the
biofunctionalized surface, which are introduced into
homogenized interface conditions linking the
Angstrom-scale of the molecule with the
micrometer-scale of the FET. By considering a
single-stranded to double-stranded DNA reaction, we
demonstrate the capability of a BioFET to detect a
certain DNA and to resolve the DNA orientation.

We have developed a topography simulation method which
combines advanced level-set techniques for surface
evolution with Monte Carlo flux calculation. The
result is an algorithm with an overall complexity
and storage requirement scaling like O(N logN)
with surface disretization. The calculation of
particle trajectories is highly optimized, since
spatial partitioning is used to accelerate ray
tracing. The method is demonstrated on Si etching in
SF6/O2 plasma.

Experiments for silicon biosensors with gate lengths in the
range of 200nm to 500nm have not been extensively
carried out. In this paper, simulations were
performed for gate lengths proportionally smaller
and greater than regular experimental gate lengths.
The sensitivity of the biosensors was simulated
using a 2D drift-diffusion model in cylindrical
coordinates using the Prophet simulator. In this
study simulated conductance results and the
respective experimental values are compared. The
good agreement between simulation and experiment
enables us to predict and optimize the sensitivity
of the DNA sensors.

The sensitivity was studied in
terms of conductance by varying the gate length,
probe spacing, binding efficiency and angle of probe
from normal.

Electrons and holes captured in self-assembled quantum dots
(QDs) are subject to symmetry breaking that cannot
be represented in with continuum material
representations. Atomistic calculations reveal
symmetry lowering due to effects of strain and
piezo-electric fields. These effects are
fundamentally based on the crystal topology in the
quantum dots. This work studies these two competing
effects and demonstrates the fine structure
splitting that has been demonstrated experimentally
can be attributed to the underlying atomistic
structure of the quantum dots.

Self-assembled quantum dots (DQ) can be grown as stacks
where the QD distance can be controlled with atomic
layer control. This distance determines the
interaction of the artificial atom states to form
artificial molecules. The design of QD stacks
becomes complicated since the structures are subject
to inhomogeneous, long-range strain and growth
imperfections such as non-identical dots and
inter-diffused interfaces. This study presents
simulations of stacks consistent of three QDs in
their resulting inhomogeneous strain field. The
simulations are performed with NEMO 3-D which uses
the valence force field method to compute the strain
and the empirical sp3d5s* tight binding method to
compute the electronic structure. Strain is shown to
provide a very interesting mixing between states and
preferred ordering of the ground state in the
top-most or bottom most quantum dot subject to
growth asymmetries.

Conventional SOI DNAFET devices, being able to detect
single-nucleotide polymor phisms, are simulated in a
comprehensive approach. These devices can be
fabricated in high-density arrays and offer
advantages compared to optical detection
methods. The influence of device parameters like
doping concentration and the size of the exposed
sensor area is investigated.

The 3-D Nanoelectronic Modeling Tool (NEMO 3-D) is an
electronic structure simulation code for the
analysis of quantum dots, quantum wells, nanowires,
and impurities. NEMO 3-D uses the Valence Force
Field (VFF) method for strain and the empirical
tight binding (ETB) for the electronic structure
calculations. Various ETB models are available,
ranging from single s orbitals (single band
effective mass), over sp3s* to sp3d5s*
models, with and without explicit representation of
spin. The code is highly optimized for operation on
cluster computing systems. Simulations of systems of
64 million atoms (strain) and 21 million atoms have
been demonstrated. This implies that every atom is
accounted for in simulation volumes of (110nm)3
and (77nm)3, respectively. Such simulations
require parallel execution on 64 itanium2 CPUs for
around 12 hours. A simple effective mass calculation
of an isolated quantum dot, in contrast, requires
about 20 seconds on a single CPU. NEMO 3-D therefore
offers the opportunity to engage both educators and
advanced researchers, utilizing a single
code. nanoHUB.org is the community web site hosted
by the Network for Computational Nanotechnology
(NCN) dedicated to bridge education, research, and
development for the whole nanoscience and
nanotechnology community. This paper reviews the
mission of the NCN exemplified by the development
and deployment of the NEMO 3-D tool.

We present an analysis of deposition of silicon nitride and
silicon dioxide layers into three-dimensional
interconnect structures. The investigations have
been performed using our general purpose topography
simulator ELSA (Enhanced Level Set Applications). We
predict void formation and its characteristics,
which play an important role for the formation of
cracks which are observed during the passivation of
layers covering IC chips.

The goal of this paper is to identify simulation models for
the deposition of silicon dioxide layers from TEOS
(tetraethoxysilane) in a CVD (chemical vapor
deposition) process and to calibrate the parameters
of these models by comparing simulation results to
SEM (scanning electron microscope) images of
deposited layers in trenches with different aspect
ratios. We describe the three models used and the
parameters which lead to the best results for each
model which allows us to draw conclusions on the
usefulness of the models.

The continued scaling of MOSFETs into the nano-scale regime
requires refined models for carrier transport due
to, e.g., unintentional doping in the active channel
region which gives rise to threshold voltage and
on-state current fluctuations. Therefore every
transport simulator which is supposed to accurately
simulate nano-devices must have a proper model for
the inclusion of the Coulomb interactions. This
paper proposes to use a 3D FMM (fast multi-pole
method) (Greengard and Rokhlin, 1997; Cheng et al.,
1999). The FMM is based on the idea of condensing
the information of the potential generated by point
sources in series expansions. After calculating
expansions in a hierarchical manner, the long-range
part of the potential is obtained by evaluating the
series at the point in question and the short-range
part is calculated by direct summation. Its
computational effort is only O(n) where n is the
number of particles. In summary, the use of the FMM
approach for semiconductor transport simulations was
validated. Simulation times are decreased
significantly and effects due to electron-electron
and electron-impurity interactions are observed as
expected. Since the FMM algorithm operates
independently of the grid used in the MC simulation,
it can be easily included into existing MC device
simulation codes.

We present the application of level set and fast marching
methods to the simulation of surface topography of a
wafer in three dimensions for deposition and etching
processes. These simulations rest on many
techniques, including a narrow band level set
method, fast marching for the eikonal equation,
extension of the speed function, transport models,
visibility determination, and an iterative equation
solver.

The aim of this work is to study the etching of trenches in
silicon and the generation of voids during the
filling of genuinely three-dimensional trench
structures with silicon dioxide or nitride. The
trenches studied are part of the manufacturing
process of power MOSFETs, where void-less filling
must be achieved. Another area of applications is
capacitance extraction in interconnect structures,
where the deliberate inclusion of voids serves the
purpose of reducing overall capacitance.
Furthermore, these simulations make it possible to
analyze the variations on the feature scale
depending on the position of the single trench on
the wafer and in the reactor.

A method for determining higher order thermal coefficients
for electrical and thermal properties of metallic
interconnect materials used in semiconductor
fabrication is presented. By applying inverse
modeling on transient electrothermal
three-dimensional finite element simulations the
measurements of resistance over time of Polysilicon
fuse structures can be matched. This method is
intended to be applied to the optimization of
Polysilicon fuses for reliability and speed.

The current challenge for TCAD is the prediction of the
performance of groups of devices, backends, and -
generally speaking - large parts of the final IC in
contrast to the simulation of single devices and
their fabrication. This enables one to predictively
simulate the performance of the final device
depending on different process technologies and
parameters, which the simulation of single devices
cannot achieve.

In this paper we focus on the
simulation of backend, interconnect capacitance, and
time delays. To that end topography simulations of
deposition, etching, and CMP processes in the
various metal lines are used to build up the backend
stack. The output of the feature scale simulations
is used as input to a capacitance extraction tool,
whose results are made available directly to the
circuit designer.

We discuss the utilized simulation
tools and their integration. The topography
simulations were performed by our tool called ELSA
(enhanced level set applications) and the subsequent
simulations by RAPHAEL. Finally simulation results
for a 100nm process are presented, where the
influence of void formation between metal lines
profoundly impacts the performance of the whole
interconnect stack.

The error of the numeric approximation of the semiconductor
device equations particularly depends on the grid
used for the discretization. Since the most
interesting regions of the device are generally
straightforward to identify, the method of choice is
to use structurally aligned grids. Here we present
an algorithm for generating structurally aligned
grids including anisotropy and for producing grids
whose resolution varies over several orders of
magnitude. Furthermore the areas with increased
resolution and the corresponding resolutions can be
defined in a flexible manner and criteria on grid
quality can be enforced.

The grid generation
algorithm was applied to sample structures which
highlight the features of this method. Furthermore
we generated grids for the simulation of a high
voltage trench gate MOSFET. In order to resolve the
junction regions accurately, four regions were
defined where the grid was grown in several
directions with varying resolutions. Finally device
simulations performed by MINIMOS NT show current
voltage characteristics and the threshold voltage.

We present a computational method for locally adapted
conformal anisotropic tetrahedral mesh
refinement. The element size is determined by an
anisotropy function which is governed by an error
estimation driven ruler according to an adjustable
maximum error. Anisotropic structures are taken into
account to reduce the amount of elements compared to
strict isotropic refinement. The spatial resolution
in three-dimensional unstructured tetrahedral meshes
for diffusion simulation can be dynamically
increased.

We present an algorithm for smoothing results of
three-dimensional Monte Carlo ion implantation
simulations and translating them from the grid used
for the Monte Carlo simulation to an arbitrary
unstructured three-dimensional grid. This algorithm
is important for joining various simulations of
semiconductor manufacturing process steps, where
data have to be smoothed or transferred from one
grid to another. Furthermore different grids must be
used since using ortho-grids is mandatory because of
performance reasons for certain Monte Carlo
simulation methods. The algorithm is based on
approximations by generalized Bernstein
polynomials. This approach was put on a
mathematically sound basis by proving several
properties of these polynomials. It does not suffer
from the ill effects of least squares fits of
polynomials of fixed degree as known from the
popular response surface method. The smoothing
algorithm which works very fast is described and in
order to show its applicability, the results of
smoothing a three-dimensional real world
implantation example are given and compared with
those of a least squares fit of a multivariate
polynomial of degree two, which yielded unusable
results.

Deposition and etching in Silicon trenches is an important
step of today’s semiconductor
manufacturing. Understanding the surface evolution
enables to predict the resulting profiles and thus
to optimize process parameters. Simulations using
the radiosity modeling approach and the level set
method provide accurate results, but their speed has
to be considered when employing advanced models and
for purposes of inverse modeling.

In this paper
strategies for increasing the accuracy of deposition
simulations while decreasing simulation times are
presented. Two algorithms were devised: first,
intertwining narrow banding and extending the speed
function yields a fast and accurate level set
algorithm. Second, an algorithm which coarsens the
surface reduces the computational demands of the
radiosity method.

Finally measurements of a typical
TEOS deposition process are compared with
simulation results both with and without coarsening
of the surface elements. It was found that the
computational effort is significantly reduced
without sacrificing the accuracy of the
simulations.

Deposition and etching of silicon trenches is an important
manufacturing step for state of the art memory
cells. Understanding and simulating the transport of
gas species and surface evolution enables to achieve
void-less filling of deep trenches, to predict the
resulting profiles, and thus to optimize process
parameters with respect to manufacturing throughput
and the quality of the resulting memory cells. For
the simulation of the SiO2 deposition process
from TEOS (Tetraethoxysilane), the level set method
was used in addition to physical models. The level
set algorithm devised minimizes computational effort
while ensuring high accuracy by intertwining narrow
banding and extending the speed function. In order
to make the predictions of the simulation more
accurate, model parameters were extracted by
comparing the step coverages of the deposited layers
in the simulation with those of SEM (scanning
electron microscope) images.

The formation and dissolution of silicon self-interstitial
clusters is linked to the phenomenon of TED
(transient enhanced diffusion) which in turn has
gained importance in the manufacturing of
semiconductor devices. Based on theoretical
considerations and measurements of the number of
self-interstitial clusters during a thermal step we
were interested in finding a suitable model for the
formation and dissolution of self-interstitial
clusters and extracting corresponding model
parameters for two different technologies (i.e.,
material parameter sets). In order to automate the
inverse modeling part a general optimization
framework was used. Additional to solving this
problem the same setup can solve a wide range of
inverse modeling problems occurring in the domain of
process simulation. Finally the results are
discussed and compared with a previous model.

Conventional macroscopic impact ionization models which use
the average carrier energy as main parameter cannot
accurately describe the phenomenon in modern
miniaturized devices. Here we present a new model
which is based on an analytic expression for the
distribution function. In particular, the
distribution function model accounts explicitly for
a hot and a cold carrier population in the drain
region of MOS transistors. The parameters are
determined by three even moments obtained from a
solution of a six moments transport model. Together
with a nonparabolic description of the density of
states accurate closed form macroscopic impact
ionization models can be derived based on familiar
microscopic descriptions.

The optimization of computationally expensive objective
functions requires approximations that preserve the
global properties of the function under
investigation. The RSM approach of using
multivariate polynomials of degree two can only
preserve the local properties of a given function
and is therefore not well-suited for global
optimization tasks. In this paper we discuss
generalized Bernstein polynomials that provide
faithful approximations by converging uniformly to
the given function. Apart from being useful for
optimization tasks, they can also be used for
solving design for manufacturability problems.

We present simulations of a recently published SRAM memory
gain cell consisting of two transistors and one MOS
capacitor, representing an alternative to
conventional six transistor SRAMs. Inverse modeling
is used to fit a given device characteristic to
measurement data. To account for de-charging due to
tunneling, we use a simple, non-local tunneling
model and calibrate it with data from literature. By
optimization, we find values for the contact
voltages in the off-region at which the retention
time is a maximum.

Experiments of As-doped poly-silicon deposition have shown
that under certain process conditions step coverages
> 1 can be achieved. We have developed a new model
for the simulation of As-doped poly-silicon
deposition, which takes into account surface
coverage dependent sticking coefficients and surface
coverage dependent As incorporation and desorption
rates. The additional introduction of Langmuir type
time-dependent surface coverage enabled the
reproduction of the bottom-up filling of the
trenches. In addition the rigorous treatment of the
time-dependent surface coverage allows to trace the
in-situ doping of the deposited film. Simulation
results are shown for poly-Si deposition into
0.1μm wide and 7μm deep, high aspect ratio
trenches.